Mathematics

17 pages, 4898 KB

Open AccessArticle

Transient Response Enhancement of PMD Battery Charger Using Rule-Based Fuzzy Logic Control

by Gijeong Yoon and Yeongsu Bak

Mathematics 2026, 14(4), 585; https://doi.org/10.3390/math14040585 (registering DOI) - 7 Feb 2026

This paper proposes a transient response enhancement of a personal mobility device (PMD) battery charger using a rule-based fuzzy logic control (RBFLC) method. PMD encompasses various applications, including electric kickboards, electric scooters, and electric wheelchairs. The rated battery voltage required for each device [...] Read more.

This paper proposes a transient response enhancement of a personal mobility device (PMD) battery charger using a rule-based fuzzy logic control (RBFLC) method. PMD encompasses various applications, including electric kickboards, electric scooters, and electric wheelchairs. The rated battery voltage required for each device is different; additionally, the PMD battery charger must be accurate and have a fast transient response. However, when the gain is significantly increased in the conventional proportional-integral (PI) control method to enhance the transient response, the battery charger output voltage exhibits oscillatory behavior and becomes unstable. Therefore, in this paper, the RBFLC method is proposed to improve the transient response performance of the battery charger without oscillation and instability of the output voltage. The proposed RBFLC method is verified through simulation and experimental results. Full article

(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)

12 pages, 345 KB

Open AccessArticle

Dynamics of Polygenic Adaptation

by Wolfgang Stephan

Mathematics 2026, 14(4), 584; https://doi.org/10.3390/math14040584 (registering DOI) - 7 Feb 2026

Abstract

Polygenic adaptation in response to natural selection on a quantitative trait has become an important topic in population genetics and evolution. We modeled a scenario in which a population was assumed to be in equilibrium between mutation, selection and genetic drift, when a [...] Read more.

Polygenic adaptation in response to natural selection on a quantitative trait has become an important topic in population genetics and evolution. We modeled a scenario in which a population was assumed to be in equilibrium between mutation, selection and genetic drift, when a sudden shift in the fitness optimum occurred. It is well known that after an environmental shift the trait mean may approach the new optimum very quickly at a rate proportional to the equilibrium genetic variance. Here, we analyze the dynamics of the allele frequencies at individual loci, using diffusion theory. We show that genetic drift slows down the speed of polygenic adaptation. We also found that, while the frequencies of rare and very common alleles decrease during the adaptive phase, alleles starting at intermediate equilibrium frequencies at the time of the optimum shift change most quickly and thus may substantially modify the shape of the allele frequency distribution. Finally, we explain how these properties of the allele frequency spectrum may be utilized in statistical tests of polygenic selection. Full article

(This article belongs to the Section E3: Mathematical Biology)

13 pages, 764 KB

Open AccessArticle

On Even Vertex Magic Total Labelings of Plus Wheels and Some Wheel-Related Graphs

by Supaporn Saduakdee and Varanoot Khemmani

Mathematics 2026, 14(4), 583; https://doi.org/10.3390/math14040583 (registering DOI) - 7 Feb 2026

Abstract

Let G be a graph with n vertices and m edges. A vertex magic total labeling of G is a bijection [...] Read more.

Let G be a graph with n vertices and m edges. A vertex magic total labeling of G is a bijection

f : V (G) \cup E (G) \to {1, 2, \dots, n + m}

such that, for each vertex

u \in V (G)

, the sum of the label of u and the labels of all edges incident to u is equal to a fixed constant, referred to as the magic constant. A vertex magic total labeling is said to be even if the labels assigned to the vertices are exactly even numbers

{2, 4, 6, \dots, 2 n}

. These labelings, along with related variations, have theoretical significance and practical applications, such as resource allocation, fault tolerance, and network design. Structured labelings aid channel assignment, address computation, and reduce collisions in networks. In this paper, we investigate wheel-related graphs that either admit or do not admit an even vertex magic total labeling. Furthermore, we introduce a new class of wheel-related graph, referred to as the plus wheel

W_{n} + r

, that can have such labelings, and we also establish a necessary and sufficient condition for such graphs to possess this property. Full article

(This article belongs to the Special Issue Graph Theory and Applications, 3rd Edition)

21 pages, 2397 KB

Open AccessArticle

Numerical Solutions via Shifted Pell Polynomials for Third-Order Rosenau–Hyman and Gilson–Pickering Equations

by Mohamed A. Abdelkawy, Waleed Mohamed Abd-Elhameed, Seham S. Alzahrani, Ahmed Gamal Atta and Anjan Biswas

Mathematics 2026, 14(3), 582; https://doi.org/10.3390/math14030582 - 6 Feb 2026

Abstract

This paper introduces a collocation algorithm for numerically solving the third-order Gilson–Pickering equation (GPE) and the classical Rosenau–Hyman equation (RHE). We employ newly developed shifted Pell polynomials as basis functions. Novel formulas for these polynomials are devised and utilized in constructing the proposed [...] Read more.

This paper introduces a collocation algorithm for numerically solving the third-order Gilson–Pickering equation (GPE) and the classical Rosenau–Hyman equation (RHE). We employ newly developed shifted Pell polynomials as basis functions. Novel formulas for these polynomials are devised and utilized in constructing the proposed algorithm. Specifically, we establish a new power form and its inversion formula, along with an explicit formula for derivatives of the shifted Pell polynomials, from which the operational matrices of derivatives (OMDs) are derived. These matrices facilitate the conversion of nonlinear dispersive models into systems of algebraic equations, efficiently solved using Newton’s iterative technique. The error analysis of the shifted Pell expansion is discussed in depth. Several numerical examples, including the RHE, its fourth-order variant, and the Fornberg–Whitham equation, are provided to demonstrate the method’s performance and accuracy. Comparative results are also reported. Full article

(This article belongs to the Special Issue Soliton Theory and Integrable Systems in Mathematical Physics)

31 pages, 4208 KB

Open AccessArticle

Study on Lateral Abutment Stress and Damage Range of Coal Seam Under the Coupling of Coal-Rock Structure

by Wenrui He, Dongdong Chen and Hengzhong Zhu

Mathematics 2026, 14(3), 581; https://doi.org/10.3390/math14030581 - 6 Feb 2026

Abstract

The lateral abutment stress and damage range of the coal seam are prerequisites for the layout of gob-side entries and surrounding rock control. They are influenced by the structure and mechanical properties of the coal seam and the overlying strata. To address this [...] Read more.

The lateral abutment stress and damage range of the coal seam are prerequisites for the layout of gob-side entries and surrounding rock control. They are influenced by the structure and mechanical properties of the coal seam and the overlying strata. To address this issue, this study establishes a mechanical analysis model for the lateral abutment stress and damage range under coupled conditions between the coal seam and overlying strata. This model systematically investigates the influence of various factors, including the fracture height and break angle of the overlying strata, the rotation angle and subsidence of key blocks, the burial depth and thickness of the coal seam, as well as the cohesion and internal friction angle of the coal mass. The study reveals that the weight and overburden load of the triangular hanging roof zone, along with the subsidence and rotation of the key blocks, are the key factors influencing the lateral abutment stress and damage range. Meanwhile, the reliability of the mechanical model has been substantiated through a combination of numerical simulation and in situ monitoring results. Full article

(This article belongs to the Special Issue Mathematics Applied in Rock Mechanics and Mining Science)

56 pages, 4119 KB

Open AccessArticle

Reliability in Robotics and Intelligent Systems: Mathematical Modeling and Algorithmic Innovations

by Madina Issametova, Nikita V. Martyushev, Boris V. Malozyomov, Anton Y. Demin, Alexander V. Pogrebnoy, Elizaveta E. Kuleshova and Denis V. Valuev

Mathematics 2026, 14(3), 580; https://doi.org/10.3390/math14030580 - 6 Feb 2026

Abstract

The rapid development of digital manufacturing and robotic systems places increased demands on the accuracy and reliability of industrial manipulators. Traditional time-based reliability metrics do not reflect the robot’s ability to consistently achieve the desired position and orientation within process tolerances or the [...] Read more.

The rapid development of digital manufacturing and robotic systems places increased demands on the accuracy and reliability of industrial manipulators. Traditional time-based reliability metrics do not reflect the robot’s ability to consistently achieve the desired position and orientation within process tolerances or the probability of the end-effector falling into a given area of permissible poses. The proposed framework integrates a deterministic kinematic model, a stochastic representation of Denavit–Hartenberg parameters and control variables, analytical methods for estimating probabilities, and numerical modeling using the Monte Carlo method. The methodology has been tested on the widely used industrial robot FANUC LR Mate 200iD/7L. The results demonstrate a significant dependence of geometric reliability on the kinematic configuration of the manipulator, with maximum reliability in compact poses and a significant reduction in elongated configurations near singularities. Comprehensive validation was carried out, including numerical experiments on a planar prototype, high-precision physical measurements on a real robot and analysis of operational data, which confirmed the adequacy of the proposed model. The developed approach provides a powerful tool for designing, optimizing and predicting the reliability of robotic cells in high-precision automation environments. Full article

(This article belongs to the Special Issue Robotics and Intelligent Systems: New Mathematical Challenges and Algorithmic Innovations)

23 pages, 5683 KB

Open AccessArticle

Optimizing RTAB-Map Viewability to Reduce Cognitive Workload in VR Teleoperation: A User-Centric Approach

by Hojin Yoon, Haegyeom Choi, Jaehoon Jeong and Donghun Lee

Mathematics 2026, 14(3), 579; https://doi.org/10.3390/math14030579 - 6 Feb 2026

Abstract

In industrial environments, providing intuitive spatial information via 3D maps is essential for maximizing the efficiency of teleoperation. However, existing SLAM algorithms generating 3D maps predominantly focus on improving robot localization accuracy, often neglecting the optimization of viewability required for human operators to [...] Read more.

In industrial environments, providing intuitive spatial information via 3D maps is essential for maximizing the efficiency of teleoperation. However, existing SLAM algorithms generating 3D maps predominantly focus on improving robot localization accuracy, often neglecting the optimization of viewability required for human operators to clearly perceive object depth and structure in virtual environments. To address this, this study proposes a methodology to optimize the viewability of RTAB-Map-based 3D maps using the Taguchi method, aiming to enhance VR teleoperation efficiency and reduce cognitive workload. We identified eight key parameters that critically affect visual quality and utilized an L18 orthogonal array to derive an optimal combination that controls point cloud density and noise levels. Experimental results from a target object picking task demonstrated that the optimized 3D map reduced task completion time by approximately 9 s compared to the RGB image condition, achieving efficiency levels approaching those of the physical-world baseline. Furthermore, evaluations using NASA-TLX confirmed that intuitive visual feedback minimized situational awareness errors and substantially alleviated cognitive workload. This study suggests a new direction for constructing high-efficiency teleoperation interfaces from a Human–Robot Interaction perspective by expanding SLAM optimization criteria from geometric precision to user-centric visual quality. Full article

(This article belongs to the Special Issue Advances in Machine Learning and Intelligent Systems)

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20 pages, 785 KB

Open AccessArticle

Pre-Disaster Preparedness in Food Bank Supply Chains Addressing Supply Uncertainty and Different Objectives

by Adrian F. Rivera, Neale R. Smith and Angel Ruiz

Mathematics 2026, 14(3), 578; https://doi.org/10.3390/math14030578 - 6 Feb 2026

Abstract

A critical decision in pre-disaster humanitarian logistics planning is determining the amount of aid to preposition to ensure timely and effective emergency response. To support managers in this process, we propose four mathematical formulations designed to optimize food prepositioning and subsequent distribution while [...] Read more.

A critical decision in pre-disaster humanitarian logistics planning is determining the amount of aid to preposition to ensure timely and effective emergency response. To support managers in this process, we propose four mathematical formulations designed to optimize food prepositioning and subsequent distribution while minimizing unmet demand under supply uncertainty. Two formulations adopt the cardinality-constrained approach: one focuses on minimizing unmet demand, and the other incorporates equity in meeting demand. The remaining two formulations are scenario-based, addressing the same objectives with and without equity considerations. To compare the variations in the solutions generated by the proposed formulations and gain a deeper understanding of their behavior and performance, the formulations are applied to synthetic instances. To assist managers in selecting the model that best aligns with their objectives, we provide a summary of the advantages and disadvantages of each formulation. Our results show that considering supply uncertainty has important implications for the total costs, and that having adequate storage capacity may help mitigate the problems caused by this uncertainty. Full article

(This article belongs to the Special Issue Simulation-Based Optimisation and Information Systems in Disaster Management)

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29 pages, 401 KB

Open AccessArticle

Dependency-Constrained Cascading Rescheduling: Network Evolution and Long-Term Adaptation

by TzeHoung Lee and Xue-Ming Yuan

Mathematics 2026, 14(3), 577; https://doi.org/10.3390/math14030577 - 5 Feb 2026

Abstract

Traditional scheduling theory optimizes initial task assignments under static assumptions, yet operational systems face repeated disruptions requiring both immediate rescheduling and long-term structural adaptation. Existing approaches treat each disruption independently, failing to capture how organizations learn and evolve through repeated challenges. This paper [...] Read more.

Traditional scheduling theory optimizes initial task assignments under static assumptions, yet operational systems face repeated disruptions requiring both immediate rescheduling and long-term structural adaptation. Existing approaches treat each disruption independently, failing to capture how organizations learn and evolve through repeated challenges. This paper presents a unified framework bridging cascading rescheduling with network evolution, formally modeling how dependency structures adapt over time to improve resilience. The framework consists of three integrated components: (1) immediate rescheduling algorithms with provable complexity bounds—O(n) for tree-structured dependencies, fixed-parameter tractable for bounded treewidth—enabling real-time response; (2) five adaptation strategies (redundancy, buffering, decoupling, reshuffling, and control) with convergence guarantees showing exponential improvement rate

O (e^{- (σ - λ) t})

; and (3) computable resilience metrics quantifying organizational capacity to absorb disruptions. Comprehensive validation through 5200 simulated weeks (52 weeks × 100 replications) demonstrates substantial performance improvements. Redundancy-based adaptation achieves 109% resilience improvement and 66% disruption reduction compared to non-adaptive baselines (

p < 0.001

, Cohen’s

d > 1.8

). The framework is implemented as Orange3 visual programming widgets, achieving 92% user acceptance among non-technical practitioners with 7-month payback periods. While the framework is domain-agnostic and applicable to any operational network with dependency constraints, validation focuses on healthcare scheduling contexts where disruption patterns are well documented. The approach demonstrates that organizations can systematically build resilience through principled adaptation rather than reactive responses, with quantifiable performance improvements and accessible implementation tools. Full article

(This article belongs to the Special Issue Data-Driven Algorithms for Optimal Decision Making in Logistics and Supply Chain Management)

18 pages, 389 KB

Open AccessArticle

Asymptotic Stability of Time-Varying Nonlinear Cascade Systems with Delay via Lyapunov–Razumikhin Approach

by Natalia Sedova and Olga Druzhinina

Mathematics 2026, 14(3), 576; https://doi.org/10.3390/math14030576 - 5 Feb 2026

Abstract

This paper addresses nonlinear time-varying cascade systems governed by differential equations with finite delay. Several sufficient conditions for asymptotic stability are derived, based on differing assumptions regarding the isolated subsystems and their interconnection. The cascade structure enables the treatment of a broad class [...] Read more.

This paper addresses nonlinear time-varying cascade systems governed by differential equations with finite delay. Several sufficient conditions for asymptotic stability are derived, based on differing assumptions regarding the isolated subsystems and their interconnection. The cascade structure enables the treatment of a broad class of systems while simplifying stability analysis compared to conventional approaches. Moreover, it allows the stabilization problem to be decoupled: under suitable conditions, the asymptotic stability of the overall cascade system follows from the stability properties of its individual subsystems. These properties are typically verified using the direct Lyapunov method. In contrast to existing results, the theorems presented herein apply to an extended class of systems and impose relaxed conditions on the Lyapunov functions employed to establish uniform asymptotic stability. Additionally, new results are provided on semiglobal exponential stability and (non-uniform) asymptotic stability for time-varying cascade systems with delay. Collectively, these contributions broaden the applicability of the direct Lyapunov method to delayed cascade systems. Full article

(This article belongs to the Special Issue Research on Delay Differential Equations and Their Applications)

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20 pages, 3823 KB

Open AccessArticle

DA-TransResUNet: Residual U-Net Liver Segmentation Model Integrating Dual Attention of Spatial and Channel with Transformer

by Kunzhan Wang, Xinyue Lu, Jing Li and Yang Lu

Mathematics 2026, 14(3), 575; https://doi.org/10.3390/math14030575 - 5 Feb 2026

Abstract

Precise medical image segmentation plays a vital role in disease diagnosis and clinical treatment. Although U-Net-based architectures and their Transformer-enhanced variants have achieved remarkable progress in automatic segmentation tasks, they still face challenges in complex medical imaging scenarios, particularly around simultaneously modeling fine-grained [...] Read more.

Precise medical image segmentation plays a vital role in disease diagnosis and clinical treatment. Although U-Net-based architectures and their Transformer-enhanced variants have achieved remarkable progress in automatic segmentation tasks, they still face challenges in complex medical imaging scenarios, particularly around simultaneously modeling fine-grained local details and capturing long-range global contextual information, which limits segmentation accuracy and structural consistency. To address these challenges, this paper proposes a novel medical image segmentation framework termed DA-TransResUNet. Built upon a ResUNet backbone, the proposed network integrates residual learning, Transformer-based encoding, and a dual-attention (DA) mechanism in a unified manner. Residual blocks facilitate stable optimization and progressive feature refinement in deep networks, while the Transformer module effectively models long-range dependencies to enhance global context representation. Meanwhile, the proposed DA-Block jointly exploits local and global features as well as spatial and channel-wise dependencies, leading to more discriminative feature representations. Furthermore, embedding DA-Blocks into both the feature embedding stage and skip connections strengthens information interaction between the encoder and decoder, thereby improving overall segmentation performance. Experimental results on the LiTS2017 dataset and Sliver07 dataset demonstrate that the proposed method achieves incremental improvement in liver segmentation. In particular, on the LiTS2017 dataset, DA-TransResUNet achieves a Dice score of 97.39%, a VOE of 5.08%, and an RVD of −0.74%, validating its effectiveness for liver segmentation. Full article

(This article belongs to the Special Issue Advances in Computer Vision and Image Processing with Applications to Bioinformatics)

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32 pages, 5567 KB

Open AccessArticle

Optimized Image Segmentation Model for Pellet Microstructure Incorporating KL Divergence Constraints

by Yuwen Ai, Xia Li, Aimin Yang, Yunjie Bai and Xuezhi Wu

Mathematics 2026, 14(3), 574; https://doi.org/10.3390/math14030574 - 5 Feb 2026

Abstract

Accurate segmentation of pellet microstructure images is crucial for evaluating their metallurgical performance and optimizing production processes. To address the challenges posed by complex structures, blurred boundaries, and fine-grained textures of hematite and magnetite in pellet micrographs, this study proposes a hybrid intelligently [...] Read more.

Accurate segmentation of pellet microstructure images is crucial for evaluating their metallurgical performance and optimizing production processes. To address the challenges posed by complex structures, blurred boundaries, and fine-grained textures of hematite and magnetite in pellet micrographs, this study proposes a hybrid intelligently optimized VGG16-U-Net semantic segmentation model. The model incorporates an improved SPC-SA channel self-attention mechanism in the encoder to enhance deep feature representation, while a simplified SAN and SAW module is integrated into the decoder to strengthen its response to key mineral regions. Additionally, a hybrid loss strategy is employed with KL regularization for training optimization. Experimental results show that the model achieves an mIoU of 85.58%, an mPA of 91.54%, and an overall accuracy of 93.58%. Compared with the baseline models, the proposed method achieves improved performance to some extent. Full article

(This article belongs to the Special Issue Mathematical Methods for Image Processing and Computer Vision)

22 pages, 1680 KB

Open AccessArticle

Application of Machine Learning to Cluster Analysis of Diabetes Mortality at the Municipality Level in Mexico According to Sociodemographic Factors

by Nelva N. Almanza-Ortega, Carlos Fernando Moreno-Calderon, Sandra Silvia Roblero-Aguilar, Rodolfo Pazos-Rangel, Joaquín Pérez-Ortega, Vanesa Landero-Nájera and Víctor Augusto Castellanos-Escamilla

Mathematics 2026, 14(3), 573; https://doi.org/10.3390/math14030573 - 5 Feb 2026

Abstract

In recent years, the mortality due to diabetes has increased around the world. In particular, diabetes is the second leading cause of mortality in Mexico, with a heterogeneous distribution of mortality rates at the municipality level. The objective of this study is the [...] Read more.

In recent years, the mortality due to diabetes has increased around the world. In particular, diabetes is the second leading cause of mortality in Mexico, with a heterogeneous distribution of mortality rates at the municipality level. The objective of this study is the analysis of clusters of municipalities with similar values for sociodemographic indices and diabetes mortality. In this sense, an application is presented that was developed using a data science methodology and a machine learning algorithm called fuzzy c-means. For this research, 4,604,360 death certificates from 2019 to 2023 were assessed, among other official data. As a result of the analysis, two key indicators related to diabetes mortality were found, i.e., one is the percentage of population in poverty and the other is population density. The main results of this research are as follows: a direct correlation was found between population density and mortality, and an inverse correlation was found between population in poverty and mortality. In the study interval, it was observed that the cluster with less mortality showed an increase in mortality rate year after year. Finally, we consider that the tendencies found can be useful to public health authorities for optimizing the distribution of resources for treating diabetes and reducing diabetes-related mortality. Full article

(This article belongs to the Special Issue Application of Artificial Intelligence, Machine Learning and Data Science in Industrial and Medical Domains)

17 pages, 2767 KB

Open AccessArticle

Implicit Neural Representation for Dense Event-Based Imaging Velocimetry

by Jia Ai, Junjie Li, Zuobing Chen and Yong Lee

Mathematics 2026, 14(3), 572; https://doi.org/10.3390/math14030572 - 5 Feb 2026

Abstract

This paper presents an Implicit Neural Representation method for Event-Based Imaging Velocimetry (INR-VG) to reconstruct dense velocity fields from sparse event streams. The core idea is to learn a mapping (multilayer perceptron) from spatial coordinates to flow velocities, [...] Read more.

This paper presents an Implicit Neural Representation method for Event-Based Imaging Velocimetry (INR-VG) to reconstruct dense velocity fields from sparse event streams. The core idea is to learn a mapping (multilayer perceptron) from spatial coordinates to flow velocities,

v (x) = f (x; θ)

, which thereby enables dense velocity measurements at any desired spatial resolution. The neural network is optimized through test-time optimization by minimizing the alignment error between warped voxel grids of events. Extensive evaluations on synthetic datasets and real-world flows demonstrate that INR-VG achieves high accuracy (errors as low as

0.05 px / ms

) and maintains robustness in challenging conditions where existing methods typically fail, including low event rates and large displacements, significantly outperforming optical-flow-based baselines. To the best of our knowledge, this work represents a successful application of implicit neural representations to event-based imaging velocimetry (EBIV), establishing a new paradigm for dense and robust event-based flow measurement. The implementation and experimental details are publicly available to support reproducibility and future research. Full article

(This article belongs to the Special Issue Applied Mathematics in Fluid Mechanics and Flows)

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25 pages, 51444 KB

Open AccessArticle

Local Contrast Enhancement in Digital Images Using a Tunable Modified Hyperbolic Tangent Transformation

by Camilo E. Echeverry and Manuel G. Forero

Mathematics 2026, 14(3), 571; https://doi.org/10.3390/math14030571 - 5 Feb 2026

Abstract

Low contrast is a frequent challenge in image analysis, especially within medical imaging and highly saturated scenes. To address this issue, we present a nonlinear transformation for local contrast enhancement in digital images. Our method adapts the hyperbolic tangent function using two parameters: [...] Read more.

Low contrast is a frequent challenge in image analysis, especially within medical imaging and highly saturated scenes. To address this issue, we present a nonlinear transformation for local contrast enhancement in digital images. Our method adapts the hyperbolic tangent function using two parameters: one to select the intensity range for modification and another to control the degree of enhancement. This approach outperforms conventional histogram-based techniques such as histogram equalization and specification in local contrast enhancement, without increasing computational cost, and produces smooth, artifact-free results in user-defined regions of interest. In addition, the proposed method was compared with CLAHE in MRIs, showing that, unlike CLAHE, the proposed method does not enhance the noise present in the background of the image. Furthermore, in deep learning contexts where dataset size is often limited, our method could serve as an effective data augmentation tool—generating varied contrast images while preserving anatomical structures, which improves neural network training for brain tumor detection in magnetic resonance imaging. The ability to manipulate local contrast may offer a pathway toward better interpretability of convolutional neural networks, as targeted contrast adjustments allow researchers to probe model sensitivity and enhance the explainability of classification and detection mechanisms. Full article

(This article belongs to the Special Issue Data Mining and Algorithms Applied in Image Processing)

17 pages, 281 KB

Open AccessFeature PaperArticle

On Aggregations of Algebraic Objects in Data Modeling

by Ivana Štajner-Papuga and Andreja Tepavčević

Mathematics 2026, 14(3), 570; https://doi.org/10.3390/math14030570 - 5 Feb 2026

Abstract

Aggregation operators are mathematical tools that, under certain constraints in the form of properties imposed on those mathematical functions, provide a representative value for the whole set of input values or structures. The question of when and what properties of input structures, with [...] Read more.

Aggregation operators are mathematical tools that, under certain constraints in the form of properties imposed on those mathematical functions, provide a representative value for the whole set of input values or structures. The question of when and what properties of input structures, with particular emphasis on fuzzy groups, and in particular

Ω

-groups, are preserved during the aggregation process is the main focus of this paper. This paper proposes a new technique for the aggregation of special fuzzy groups in a lattice-valued framework based on the aggregation of lattice-valued weak equivalence relations. Necessary and sufficient conditions for aggregation operators on complete lattices to aggregate

Ω

-groups is the main result. Full article

(This article belongs to the Section A: Algebra and Logic)

24 pages, 1924 KB

Open AccessArticle

Simultaneous Confidence Intervals for Pairwise Differences of Means in Zero-Inflated Rayleigh Distributions with an Application to Road Accident Fatalities Data

by Warisa Thangjai, Sa-Aat Niwitpong, Narudee Smithpreecha and Arunee Wongkhao

Mathematics 2026, 14(3), 569; https://doi.org/10.3390/math14030569 - 5 Feb 2026

Abstract

This paper develops simultaneous confidence intervals (SCIs) for pairwise differences of means with zero-inflated Rayleigh (ZIR) distributions, a flexible framework for modeling positively skewed data with excess zeros. Closed-form expressions for the ZIR mean are derived, and several competing interval estimation procedures are [...] Read more.

This paper develops simultaneous confidence intervals (SCIs) for pairwise differences of means with zero-inflated Rayleigh (ZIR) distributions, a flexible framework for modeling positively skewed data with excess zeros. Closed-form expressions for the ZIR mean are derived, and several competing interval estimation procedures are investigated, including generalized confidence interval (GCI), parametric bootstrap (PB), method of variance estimates recovery (MOVER), delta-method normal approximation, and highest posterior density (HPD) intervals. The finite-sample performance of the proposed SCIs is examined via extensive Monte Carlo simulations, focusing on empirical coverage probabilities (CPs) and average interval lengths (ALs) over a broad range of parameter configurations and zero-inflation levels. A real data application to road accident fatality counts demonstrates the practical utility of the proposed methodology. The results show that the HPD method consistently achieves the most favorable balance between coverage accuracy and interval efficiency. Overall, this study advances reliable simultaneous inference for zero-inflated models commonly encountered in environmental, biomedical, and reliability studies. Full article

(This article belongs to the Special Issue Statistical Inference: Methods and Applications)

17 pages, 2265 KB

Open AccessArticle

Current Transformer Error Compensation Under Core Saturation Conditions Based on Machine Learning Algorithms

by Ismoil Odinaev, Svetlana Beryozkina, Andrey Pazderin, Mihail Senyuk, Murodbek Safaraliev and Pavel Dubrovin

Mathematics 2026, 14(3), 568; https://doi.org/10.3390/math14030568 - 5 Feb 2026

Abstract

To provide information support for relay protection and emergency automation algorithms, electromagnetic measuring voltage and current transformers are most often used. As practice shows, the magnetic core of the current transformers can be saturated under transient processes. This negatively impacts the proper functioning [...] Read more.

To provide information support for relay protection and emergency automation algorithms, electromagnetic measuring voltage and current transformers are most often used. As practice shows, the magnetic core of the current transformers can be saturated under transient processes. This negatively impacts the proper functioning of protection systems. This paper proposes a methodology for restoration of the current transformers’ secondary current based on machine learning algorithms. The task of current restoration is reduced to clustering and regression problems. The groups’ current data are clustered depending on the depth of core saturation and the shape of current distortion. Then, solving the regression problem, current restoration is performed. Considering the requirements for the performance of the protection system, the following machine learning algorithms were selected for current recovery: Decision Tree, Random Forest, XGBoost, and Support Vector Machine for regression problems. The results of computational experiments show that the optimal number of clusters is four. Among the current restoration algorithms, XGBoost proved to be the most suitable. On average, for 17,240 test saturation modes, its error was 4%. The time delay for restoration one saturation mode was 0.0067 ms. Full article

(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering, 2nd Edition)

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14 pages, 8558 KB

Open AccessArticle

FDEA-Net: Enhancing X-Ray Fracture Detection via Detail-Boosted and Rotation-Aware Feature Encoding

by Xiaohan Yu, Meng Wang and Chao He

Mathematics 2026, 14(3), 567; https://doi.org/10.3390/math14030567 - 5 Feb 2026

Abstract

X-ray imaging is the most widely used modality for fracture diagnosis in clinical practice due to its efficiency and accessibility. However, automated X-ray fracture detection faces two major challenges. First, fracture regions often contain subtle and low-contrast crack patterns, making it difficult for [...] Read more.

X-ray imaging is the most widely used modality for fracture diagnosis in clinical practice due to its efficiency and accessibility. However, automated X-ray fracture detection faces two major challenges. First, fracture regions often contain subtle and low-contrast crack patterns, making it difficult for models to capture essential fine details. Second, fractures exhibit strong directional variability, while conventional detection frameworks have limited capacity to model rotation changes. To address these issues, we propose FDEA-Net, an enhanced detection framework tailored for fracture analysis. It integrates two lightweight improvement modules. The Fracture Detail Enhancer (FDE) strengthens high-frequency textures and fine-grained structural cues that are closely associated with fracture lines. The Rotation Aware Encoder (RAE) encodes rotation-sensitive representations, improving recognition under diverse fracture orientations. Experiments on a large-scale X-ray fracture dataset show clear performance gains, achieving an mAP50 of 0.742 and an F1-score of 0.738. These findings verify the effectiveness of combining detail enhancement with rotation-aware feature modeling. FDEA-Net provides an efficient and generalizable solution for reliable detection of subtle fractures in medical imaging. Full article

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